Executive functions (EFs) are high-level cognitive processes that allow us to coordinate our actions, thoughts, and emotions, enabling us to perform complex tasks. An increasing number of studies have highlighted the role of EFs in building a solid foundation for subsequent development and learning and shown that EFs are associated with good adjustment and academic skills. The main objective of this study was to analyze whether EF levels in 44 Spanish children in the last year of preschool were associated with levels of literacy and math skills the following year, that is, in the first year of compulsory education. We used a multi-method design, which consisted of systematic observation to observe preschool children during play and selective methodology to assess their reading, writing, and math skills in the first year of compulsory primary education. General linear modeling was used to estimate the percentage of variability in academic skills in the first year of primary school that was explained by preschool EF abilities. The results showed that preschool EF level, together with participants and the instrument used to assess academic skills, explained 99% of the variance of subsequent academic performance. Another objective was to determine whether our findings were generalizable to the reference population. To make this determination, we estimated the optimal sample size for assessing preschool EFs. To do this, we performed a generalizability analysis. The resulting generalizability coefficient showed that our sample of 44 students was sufficient for assessing preschool EFs. Therefore, our results are generalizable to the reference population. Our results are consistent with previous reports that preschool EF abilities may be associated with subsequent literacy and math skills. Early assessment of EFs may therefore contribute to identifying children who are likely to experience later learning difficulties and guide the design of suitable interventions for the optimization of EFs.